I'm thinking of a number. When my number is divided by 5 the remainder is 4. When my number is divided by 3 the remainder is 2. Can you find my number?

The number 8888...88M9999...99 is divisible by 7 and it starts with the digit 8 repeated 50 times and ends with the digit 9 repeated 50 times. What is the value of the digit M?

6! = 6 x 5 x 4 x 3 x 2 x 1. The highest power of 2 that divides exactly into 6! is 4 since (6!) / (2^4 ) = 45. What is the highest power of two that divides exactly into 100!?

Find the highest power of 11 that will divide into 1000! exactly.

Find the number which has 8 divisors, such that the product of the divisors is 331776.

When the number x 1 x x x is multiplied by 417 this gives the answer 9 x x x 0 5 7. Find the missing digits, each of which is represented by an "x" .

Using the digits 1, 2, 3, 4, 5, 6, 7 and 8, mulitply a two two digit numbers are multiplied to give a four digit number, so that the expression is correct. How many different solutions can you find?

This problem is designed to help children to learn, and to use, the two and three times tables.

When I type a sequence of letters my calculator gives the product of all the numbers in the corresponding memories. What numbers should I store so that when I type 'ONE' it returns 1, and when I type. . . .

The number 12 = 2^2 × 3 has 6 factors. What is the smallest natural number with exactly 36 factors?

Can you find what the last two digits of the number $4^{1999}$ are?

What is the largest number you can make using the three digits 2, 3 and 4 in any way you like, using any operations you like? You can only use each digit once.

Amazing as it may seem the three fives remaining in the following `skeleton' are sufficient to reconstruct the entire long division sum.

Choose any 3 digits and make a 6 digit number by repeating the 3 digits in the same order (e.g. 594594). Explain why whatever digits you choose the number will always be divisible by 7, 11 and 13.

The number 10112359550561797752808988764044943820224719 is called a 'slippy number' because, when the last digit 9 is moved to the front, the new number produced is the slippy number multiplied by 9.

Resources to support understanding of multiplication and division through playing with number.

56 406 is the product of two consecutive numbers. What are these two numbers?

In November, Liz was interviewed for an article on a parents' website about learning times tables. Read the article here.

The Scot, John Napier, invented these strips about 400 years ago to help calculate multiplication and division. Can you work out how to use Napier's bones to find the answer to these multiplications?

Find out what a Deca Tree is and then work out how many leaves there will be after the woodcutter has cut off a trunk, a branch, a twig and a leaf.

Use 4 four times with simple operations so that you get the answer 12. Can you make 15, 16 and 17 too?

This big box multiplies anything that goes inside it by the same number. If you know the numbers that come out, what multiplication might be going on in the box?

Work out Tom's number from the answers he gives his friend. He will only answer 'yes' or 'no'.

On the planet Vuv there are two sorts of creatures. The Zios have 3 legs and the Zepts have 7 legs. The great planetary explorer Nico counted 52 legs. How many Zios and how many Zepts were there?

All the girls would like a puzzle each for Christmas and all the boys would like a book each. Solve the riddle to find out how many puzzles and books Santa left.

Which is quicker, counting up to 30 in ones or counting up to 300 in tens? Why?

After training hard, these two children have improved their results. Can you work out the length or height of their first jumps?

What is the lowest number which always leaves a remainder of 1 when divided by each of the numbers from 2 to 10?

This article for teachers looks at how teachers can use problems from the NRICH site to help them teach division.

Can you see how these factor-multiple chains work? Find the chain which contains the smallest possible numbers. How about the largest possible numbers?

Look at what happens when you take a number, square it and subtract your answer. What kind of number do you get? Can you prove it?

There are four equal weights on one side of the scale and an apple on the other side. What can you say that is true about the apple and the weights from the picture?

Visitors to Earth from the distant planet of Zub-Zorna were amazed when they found out that when the digits in this multiplication were reversed, the answer was the same! Find a way to explain. . . .

Given the products of adjacent cells, can you complete this Sudoku?

Number problems at primary level that may require determination.

Using the numbers 1, 2, 3, 4 and 5 once and only once, and the operations x and ÷ once and only once, what is the smallest whole number you can make?

Are these statements always true, sometimes true or never true?

Can you complete this calculation by filling in the missing numbers? In how many different ways can you do it?

Can you work out some different ways to balance this equation?

Use your logical reasoning to work out how many cows and how many sheep there are in each field.

Take the number 6 469 693 230 and divide it by the first ten prime numbers and you'll find the most beautiful, most magic of all numbers. What is it?

Have a go at balancing this equation. Can you find different ways of doing it?

Here is a picnic that Petros and Michael are going to share equally. Can you tell us what each of them will have?

If you take a three by three square on a 1-10 addition square and multiply the diagonally opposite numbers together, what is the difference between these products. Why?

Find the smallest whole number which, when mutiplied by 7, gives a product consisting entirely of ones.

Mathematicians are always looking for efficient methods for solving problems. How efficient can you be?